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ρ ab =Γ [abΓ cd]ρ cd consequence of Rarita-Schwinger =Γ [cdΓ ab]ρ cd =Γ [cd α α(G 4) ab] cd by component of G4 Bianchi \begin{array}{l} \rho_{a b} \\ \;=\; \Gamma_{[a b} \Gamma_{c d]} \rho^{c d} & \text{consequence of Rarita-Schwinger} \\ \;=\; \Gamma_{[c d} \Gamma_{a b]} \rho^{c d} \\ \;=\; \Gamma^{\bullet \alpha}_{[c d}\, \nabla_\alpha (G_4)_{a b]}{}^{c d} & \text{by component of G4 Bianchi } \end{array}

Typing “$ X ⟜ Y$” gives “XY X ⟜ Y

Last revised on March 18, 2024 at 09:17:09. See the history of this page for a list of all contributions to it.